NCERT Solutions for Class 8 Maths Chapter 11 Exercise 11.4 (Ex. 11.4) Mensuration free in Hindi or English Medium updated for new academic session 2022-2023. In this exercise, we have to go through the concept of area and volume of cylinder. Exercise 11.4 of 8th Maths is based on application of cylindrical objects. Videos and PDF file format solutions are available to use free without any login or password.

## Class 8 Maths Chapter 11 Exercise 11.4 Solution

 Class: 8 Mathematics Chapter: 11 Mensuration Exercise: 11.4 Videos and PDF Solution

### Class 8 Maths Chapter 11 Exercise 11.4 Solution in Videos

Class 8 Maths Chapter 11 Exercise 11.4 Solution
Class 8 Maths Chapter 11 Exercise 11.4 Explanation

#### Right Circular Cylinder

The length between the two ends is called the length or the height of the cylinder. If the axis of the cylinder is perpendicular to each cross-section, then the cylinder is called a right circular cylinder.

The radius of the cross section of a cylinder is called the radius of the cylinder. A cylinder has two circular ends.

##### Base of Circular Cylinder

The line joining the centres of these two ends is called the axis of the cylinder. The circular end on which the cylinder rests is called its base.

##### Lateral Surface of Right Circular Cylinder

The curved surface which joins two bases of a right circular cylinder is called its lateral surface. Here, by a cylinder, we would mean a right circular cylinder.

##### Formulae for Volume and Surface Area of a Cylinder

Let us consider a cylinder of height = h units and bade radius = r units. Them, we have:
(i) Volume of the cylinder = (πr2h) cubic units
(ii) Curved (lateral) surface area of the cylinder = (2πrh) sq. units
(iii) Total surface area of the cylinder = (2πrh + 2πr2) sq. units = 2πr (h + r) sq. units

### Fine the volume, curved surface area and the total surface area of a cylinder having base radius 10.5 cm and height 18 cm.

Here, r = 10.5 cm = 21/2 cm and h = 18 cm.
Volume of the cylinder = (πr2h) cubic units
= (22/7 x 21/2 x 21/2 x 18) = 6237 cm³
Curved surface area of the cylinder = (2πrh) sq units
(2 x 22/7 x 21/2 x 18) = 1188 cm²
Total surface area of the cylinder = 2πr (h + r) sq units
(2 x 22/7 x 21/2 x (18 + 21/2) = 1881 cm²

### How many cubic metres of earth must be dug out to sink a well which is 16 m deep and which has a radius of 3.5? If the earth taken out is spread over a rectangular plot of dimensions 25 m x 16 m, what is the height of the platform so formed?

Here, r = 3.5 m = m and h = 16 m.
Volume of the earth dug out = (πr2h) cubic units
= 22/7 x 7/2 x 7/2 x 16 m³ = 616 m³
Area of the platform = (25 x 16) m² = 400 m²
Volume of the platform formed = volume of the earth dug out = 616 m³
Height of the platform = volume/area
= 616/400 m = 1.54 m
Hence, the height of the platform formed is 1.54 m

### What is special about a cylinder?

A cylinder is a geometric solid that is very common in everyday life, such as a soup can. If you take it apart you find it has two ends, called bases, that are usually circular. The bases are always congruent and parallel to each other.

### What is a cylinder composed of?

A cylinder is a solid composed of two congruent circles in parallel planes, their interiors and all the line segments parallel to the segment containing the centers of both circles with endpoints on the circular regions. The circles and their interiors are the bases. The radius of the cylinder is the radius of a base.

### What is cylinder in math definition?

In mathematics, a cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.      